We calculate the single-particle resonances in a spherical Woods-Saxon potential using real stabilization method. The box discretization method is used to find positive energy states of the Woods-Saxon potential. The discretized positive energy is stabilized against the box size when a resonance condition is met. The phase shifts are calculated by using the wave functions thus obtained. The resonance parameters could be calculated through fitting the energies and phase shifts in resonance region to the Wigner formula.